1. Field of the Invention
The present invention concerns computer-implemented and/or computer-enabled methods, systems, and mediums for enabling improved control of errors during process control. More specifically, one or more embodiments of the present invention relate to distinguishing a variance due to white noise from a statistical process variance measured during process control, particularly in connection with semiconductor manufacturing.
2. Description of the Related Art
Detecting and controlling errors during a manufacturing process is an important goal. This is particularly true in connection with the process of manufacturing semiconductors. During the manufacturing process, various measurements are made in order to detect and/or determine errors, e.g., to detect when an observed value differs significantly from an intended target result. When the difference is sufficient, the manufacturing process control system will attempt to control (e.g., compensate for) the error so as to continue to produce products (e.g., chips) that are within acceptable ranges or tolerances from the target result.
In general, it has been observed that semiconductor devices processed in connection with a semiconductor manufacturing process will inevitably include at least some error or some deviation from the intended target result or specification. In order to determine when it is desired to perform additional control in order to make an adjustment during processing, conventional systems utilize a threshold value as a trigger. Whenever the additional control is triggered and the adjustment is made, however, the result following the adjustment still will usually deviate from the intended target result. Further, there are tolerances within which a tighter adjustment of a control does not effectively cause the material to be processed closer to specification, since the control is simply not capable of a sufficiently fine adjustment.
Conventionally, control of an error is attempted when one or more preconditions assigned to a tolerance range for the target specification, are evaluated using a statistical approach and are satisfied. The conventional statistical approach employs a standard deviation. Nevertheless, even when the process control system uses standard deviation as the threshold value, there is always a lack of precision, or a tolerance range within which it is not truly possible to control more tightly.
A significant reason often preventing tolerance ranges from being controlled more tightly is that some portion of the measurement, including the amount of observed value which is determined to be error, may actually be due to “white noise”. White noise does not necessarily represent an “error”. White noise represents an uncontrollable (and typically temporary) fluctuation in measurement. One example of white noise in a semiconductor manufacturing system is a sudden and temporary disturbance in ambient temperature, which is neither measured nor controlled, but would result in a change in thickness of the product. When determining whether an error occurred and/or how much (and whether) to compensate for any difference from the desired target result and/or to control an error that may occur during the manufacturing process, white noise should be taken into account.
The true amount of white noise occurring during manufacturing processes is not easily determined. In order to accommodate or adjust for white noise, the semiconductor industry conventionally utilizes a statistical process variance, or standard deviation, determined at optimal conditions, as an estimation of white noise. Thus, statistical process variance that is used as a substitute for what would otherwise be a truer (e.g., more real world) measurement of a general type of white noise is measured while the process, material to be processed, and processing device conditions are at an atypically pristine state. This type of measurement of white noise at pristine conditions yields a measurement during a best looking steady state performance, reflecting what cannot be controlled even at the best of conditions. The measurement at these atypical conditions is then utilized as an estimation of the white noise occurring throughout the manufacturing process under consideration.
The problem with the aforementioned conventional use of measurements at pristine conditions as a white noise estimate, despite its industry acceptance, is that it is not a reasonably accurate reflection of white noise that occurs during real manufacturing conditions. One of many reasons that measurements at pristine conditions do not reasonably reflect true conditions is that materials such as wafers processed in most front and back end processing devices in the semiconductor industry have relationships with or effects on subsequently processed wafers. Accordingly, for example, conditions applied to wafers that were previously processed in a processing device will have residual effects on wafers that are currently being processed in that processing device. An estimation of white noise derived from measurements taken while the processing device is at a steady state, consequently, does not reflect the fluctuations introduced during real-world run-to-run processing.
Regarding the aforementioned conventional techniques, statistical use of standard deviation in connection with observed deviation is illustrated, for example in “Statistical feedback control of a plasma etch process”, P. Mozumder et al., IEEE Transactions on Semiconductor Manufacturing, Vol. 7, No. 1 (February 1994) (incorporated herein by reference). The statistical variance Sk at the kth run is calculated using the standard deviation as:
                              s          k                =                                            1                              n                -                1                                      ⁡                          [                                                                    ∑                                          i                      =                      1                                        n                                    ⁢                                      X                                          k                      -                      i                      +                      1                                        2                                                  -                                  n                  ⁢                                                                          ⁢                                                            (                                              X                        _                                            )                                        2                                                              ]                                                          (        1        )            
where
n=number of samples
X=deviation of observed value from predicted value
As can be seen, the standard deviation calculation does not distinguish between systematic variation and white noise variation components of the error. Hence, conventionally both the systematic and white noise variations are controlled together, rather than separately.
The conventional process control system thus compares this observed “combined” standard deviation to a threshold in order to determine if the deviation is unacceptable. Once the standard deviation greater than the threshold is detected, a tuning procedure in the process model is invoked in order to appropriately control the deviation. In essence, standard deviation-based methods only act to control when the standard deviation range is outside a particular threshold or trigger. In the conventional process control method, the standard deviation is used to determine the level for the threshold or trigger. Within the threshold, it is assumed that the deviation cannot be sufficiently controlled.
Therefore, there remains a need to have improved control, particularly within a tolerance range associated with a target specification. There also remains a need to address the effects of run-to-run conditions on such measurements.